Circumference Calculator

Calculate circumference, arc length, and all circle properties.

Enter 360° for full circle, or less for arc calculations

Circumference and Arc Length Formulas

The circumference of a circle is the distance around its edge. An arc is a portion of the circumference, and its length depends on the central angle.

Basic Formulas

  • Circumference: C = 2Ï€r = Ï€d (where r = radius, d = diameter)
  • Area: A = Ï€r²
  • Radius from Circumference: r = C / (2Ï€)
  • Radius from Area: r = √(A / Ï€)

Arc Length Formulas

  • Arc Length (degrees): Arc = (θ / 360) × 2Ï€r (where θ = angle in degrees)
  • Arc Length (radians): Arc = θ × r (where θ = angle in radians)
  • Arc Percentage: (θ / 360) × 100%

Examples

Example 1: Circle with radius 5

• Circumference = 2π(5) = 31.42

• Area = π(5)² = 78.54

Example 2: Arc with radius 10 and angle 90°

• Arc Length = (90/360) × 2π(10) = 15.71

• Arc Percentage = (90/360) × 100 = 25%

Note: This calculator uses π ≈ 3.14159 for precise calculations. All results are displayed with 4 decimal places for accuracy.

This calculator provides mathematical calculations for circles and arcs based on standard geometric formulas. Results are accurate to four decimal places. While we strive for accuracy, please verify important calculations independently. This tool is for educational and informational purposes.

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